arXiv:2610. 13461v1 Announce Type: new Abstract: AI systems are making rapid progress in mathematics, but this progress is hard to measure.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.
The paper presents a bounded, online step-level repair module for Lean 4 that uses compiler error messages to fix rejected tactics instead of discarding them. By sampling up to $K$ candidate tactics and allowing at most $R$ repairs per step, the method improves solve rates over a sampling-only baseline, achieving up to a 32% relative gain and solving 82 additional theorems on a 1,990-theorem subset of the LeanDojo benchmark. The approach trades extra runtime for reachable proofs, with most benefit coming from early repair attempts and shallow tactic failures, and it successfully replicates on the Lean Workbook benchmark, nearly doubling its solve rate without regressions.
arXiv:2605. 22148v3 Announce Type: replace Abstract: A large language model (LLM) agent that writes and edits its own skill library must also decide which skills to keep, from one noisy scalar per skill.
arXiv:2610. 12211v1 Announce Type: new Abstract: A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications.
The paper addresses the asymmetry in verifying optimality claims for synthesis pipelines, distinguishing between the upper bound (existence of a program) and the lower bound (non-existence of a smaller program). It introduces a pipeline that synthesizes minimal linear straight‑line programs over GF(2) and produces DRAT proofs for every UNSAT result, thereby closing the so‑called refutation gap for 121 previously uncertified optimality claims. The authors report that the median proof size is 1.1 MB, checking takes 1.9× the solving time, and that their verification process uncovered defects missed by code review, highlighted interface obstacles, and exposed a budget‑related audit failure.
arXiv:2406. 13668v4 Announce Type: replace Abstract: A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made.
The paper introduces a formal framework for agent harnesses that guarantees termination, prevents drift, and enforces spend limits through bounded loops, gates, and repair relations. It proves that these guarantees hold even with repair budgets and demonstrates the effectiveness of the system by identifying vacuous gates and achieving low false‑accept rates in a 69‑loop catalogue. The authors provide an instrumented implementation and a held‑out mutant corpus to validate gate correctness.